Publication result detail

Construction and Optimization of Stability Conditions of Learning Processes in Mathematical Models of Neurodynamics

DIBLÍK, J.; SHATYRKO, A.; KHUSAINOV, D.; OLEKSII, B.; BAŠTINEC, J.

Original Title

Construction and Optimization of Stability Conditions of Learning Processes in Mathematical Models of Neurodynamics

English Title

Construction and Optimization of Stability Conditions of Learning Processes in Mathematical Models of Neurodynamics

Type

Paper in proceedings (conference paper)

Original Abstract

This article is devoted to dynamic processes in the field of artificial intelligence, namely in the tasks of neurodynamics: the field of knowledge in which neural networks are considered as nonlinear dynamical systems and focuses on the problem of stability. The systems under consideration share four common characteristics: a large number of nodes (neurons), nonlinearity, dissipativity, noise. The purpose of this work is to build to construct of asymptotic stability conditions for dynamic model of neuronet network, which is described in terms of ODE nonlinear systems. Main method of investigation is Lyapunov direct method. Authors show that solution of pointed problem can be reduced to the task of convex optimization. By realization on Python tools the algorithm of Nelder-Mead method, a number of numerical experiments were conducted to select the optimal parameters of the Lyapunov function.

English abstract

This article is devoted to dynamic processes in the field of artificial intelligence, namely in the tasks of neurodynamics: the field of knowledge in which neural networks are considered as nonlinear dynamical systems and focuses on the problem of stability. The systems under consideration share four common characteristics: a large number of nodes (neurons), nonlinearity, dissipativity, noise. The purpose of this work is to build to construct of asymptotic stability conditions for dynamic model of neuronet network, which is described in terms of ODE nonlinear systems. Main method of investigation is Lyapunov direct method. Authors show that solution of pointed problem can be reduced to the task of convex optimization. By realization on Python tools the algorithm of Nelder-Mead method, a number of numerical experiments were conducted to select the optimal parameters of the Lyapunov function.

Keywords

Neuronet model; differential equation system; software; stability; Lyapunov function.

Key words in English

Neuronet model; differential equation system; software; stability; Lyapunov function.

Authors

DIBLÍK, J.; SHATYRKO, A.; KHUSAINOV, D.; OLEKSII, B.; BAŠTINEC, J.

RIV year

2024

Released

02.12.2022

Publisher

CEUR-WS

Book

9th International Scientific Conference "Information Technology and Implementation"

ISBN

1613-0073

Periodical

CEUR Workshop Proceedings

State

Federal Republic of Germany

Pages from

1

Pages to

10

Pages count

10

BibTex

@inproceedings{BUT187326,
  author="Andrej {Shatyrko} and Denys Ya. {Khusainov} and Bychkov {Oleksii} and Josef {Diblík} and Jaromír {Baštinec}",
  title="Construction and Optimization of Stability Conditions of Learning Processes in Mathematical Models of Neurodynamics",
  booktitle="9th International Scientific Conference {"}Information Technology and Implementation{"}",
  year="2022",
  journal="CEUR Workshop Proceedings",
  pages="1--10",
  publisher="CEUR-WS",
  issn="1613-0073"
}